The thought occurs to me that they could always pulls some shenanigans where you think you’re taking on the Justice League, but it turns out to be imposters of some kind - perhaps the Crime Syndicate.
Something like that would not only serve the purposes of letting the SS take on the “Justice League,” but also allow them to be more ruthlessly effective villains singularly, but plagued by infighting and backstabbing as a group - thus allowing for a mission where the entire SS takes on “Green Lantern”/Power Ring, and he cant call for help.
Just spitballing, here. There’s not a lot of good ways to have the SS vs the Justice League as a straight up premise.